MinT - Best Known (168−39, 168, s)-Nets in Base 3

Best Known (168−39, 168, s)-Nets in Base 3

(168−39, 168, 464)-Net over F₃ — Constructive and digital

Digital (129, 168, 464)-net over F₃, using

t-expansion [i] based on digital (128, 168, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 42, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(168−39, 168, 985)-Net over F₃ — Digital

Digital (129, 168, 985)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−39, 168, 61901)-Net in Base 3 — Upper bound on s

There is no (129, 168, 61902)-net in base 3, because

1 times m-reduction [i] would yield (129, 167, 61902)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47 789185 078535 030872 015690 592246 815966 050620 665551 695342 367329 225880 428744 487969 > 3¹⁶⁷ [i]